Compound interest

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nidhis.1408: Master | Next Rank: 500 Posts; Posts: 135; Joined: Mon Oct 03, 2011 6:54 amFollowed by: 4 members

by nidhis.1408 » Sat Sep 29, 2012 10:54 am

An investment is compounded annualy at 12.5% interest. If after 3 years, it is worth $1458, what was the initial investment?
A. $1024
B. $1048
C. $1096
D. $1128
E .$1162

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Source: Beat The GMAT — Problem Solving | Sat Sep 29, 2012 10:54 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Sat Sep 29, 2012 11:33 am

nidhis.1408 wrote:An investment is compounded annualy at 12.5% interest. If after 3 years, it is worth $1458, what was the initial investment?
A. $1024
B. $1048
C. $1096
D. $1128
E .$1162

In the formula
Final Amount = P(1 + R/100)^n

R = 12.5
n = 3 because the principal will be compounded thrice.

1458 = P(1 + 12.5/100)^3
1458 = P(9/8)^3
P = 1458 (8/9)^3
P = 2 (8)^3 = 2^10 = 1024

[spoiler](A)[/spoiler] is correct.

Aneesh Bangia
GMAT Math Coach
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 29, 2012 5:40 pm

nidhis.1408 wrote:An investment is compounded annualy at 12.5% interest. If after 3 years, it is worth $1458, what was the initial investment?
A. $1024
B. $1048
C. $1096
D. $1128
E .$1162

12.5% = 1/8.
Over 3 years, the initial investment increases by 1/8 THREE TIMES.
Since the resulting amount is an INTEGER, the initial investment must be a value that can be multiplied by 1/8 -- in other words, DIVIDED by 8 -- three times.
Thus, the initial investment must be a multiple of 8Â³ = 512.
Only answer choice A is a multiple of 512.

The correct answer is A.

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